Finite Group Databasebeta

← C11×#60612 #14637805

Subgroups — C11×#60612 #14637805

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3458C211yesmaximal, characteristic, complemented
2C11×#3449C211yesmaximal, characteristic
3C11×#3137C218yesmaximal, complemented
4C11×#3136C218yesmaximal, complemented
5C11×#3135C214yesmaximal, complemented
6C11×#3131C214yesmaximal, complemented
7C11×#2896C212yesmaximal, complemented
8C2×C11×#416C212yesmaximal, complemented
9C2×C11×#405C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C11×#544—22no—
14C11×#544C2218yescomplemented
15C11×#543—22no—
16C11×#537—22no—
17C11×#536C2214yes—
18C11×#535C2214yes—
19C11×#534—22no—
20C11×#533—24no—
21C11×#533C2214yescomplemented
22C11×#532C2214yes—
23C11×#525—24no—
24C2×C11×#117C2212yes—
25C2×C11×#117C2211yescharacteristic
26C11×#491C2218yescomplemented
27C11×#490C2218yescomplemented
28C11×#489C22116yescomplemented
29C11×#488C22116yescomplemented
30C11×#487C2218yescomplemented
31C11×#486C2218yescomplemented
32C11×#419C2214yescomplemented
33C11×#418C2214yescomplemented
34C11×#417C2218yes—
35C11×#416C2218yes—
36C11×#416C2214yescomplemented
37C11×#416C2214yescomplemented
38C11×#416C2218yescomplemented
39C2×C11×#103C2214yescomplemented
40C2×C11×#102C2214yescomplemented
41C11×#405C2218yescomplemented
42C2×C11×#97C2212yescomplemented
43C2×C4×C8×C11C2212yescomplemented
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—28no—
47C2×C11×#41—28no—
48C2×C11×#41C2314yes—
49C2×C11×#41C2314yes—
50C22×Q8×C11C2312yes—
51C22×D4×C11—22no—
52C22×D4×C11C2312yes—
53C23×C4×C11—22no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—24no—
56C2×C11×M16C2314yes—
57C22×C8×C11—24no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2314yes—
62C11×C4⋊Q8—28no—
63C11×C4⋊Q8C2314yes—
64C11×C4⋊Q8C2318yes—
65C11×#127C2314yes—
66C11×#125—28no—
67C11×#125C2318yes—
68C11×#124C2318yes—
69C11×#123—28no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—216no—
73C11×#121—28no—
74C11×#121—28no—
75C11×#120—28no—
76C4×Q8×C11—28no—
77C4×D4×C11—28no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117D414yes—
81C11×#117C2314yes—
82C11×#117C2314yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—22no—
89C2×C42×C11C2312yes—
90C11×#103C2318yes—
91C11×#103C23116yes—
92C11×#103C2318yes—
93C11×#102C2318yes—
94C11×#102C23116yes—
95C11×#102C2318yes—
96C11×#97C2318yes—
97C4×C8×C11C2318yes—
98#60612C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—22no—
100C24×C11C2×D411yescharacteristic
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—28no—
105C11×#41—48no—
106C11×#41—48no—
107C2×Q8×C11—22no—
108C2×Q8×C11—28no—
109C2×Q8×C11—24no—
110C2×Q8×C11—24no—
111C2×Q8×C11C2414yes—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—28no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—48no—
119C2×D4×C11C2414yes—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—48no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11#4114yes—
129C22×C4×C11#4114yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2411yescharacteristic
132C11×M16—28no—
133C2×C8×C11—28no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—24no—
137C2×C8×C11C2412yes—
138C2×C8×C11C2414yes—
139C2×C8×C11C2412yes—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—216no—
144C11×C4⋊C4C2×D418yes—
145C11×C4⋊C4C2418yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—216no—
149C11×C22⋊C4C2×D418yes—
150C42×C11—24no—
151C42×C11—24no—
152C42×C11C2×D414yes—
153C42×C11C2414yes—
154#3458C2×C1111yescharacteristic, complemented
155#3449C2×C1111yescharacteristic
156#3137C2×C1118yescomplemented
157#3136C2×C1118yescomplemented
158#3135C2×C1114yescomplemented
159#3131C2×C1114yescomplemented
160#2896C2×C1112yescomplemented
161C2×#416C2×C1112yescomplemented
162C2×#405C2×C1111yescharacteristic, complemented
163C23×C11—24no—
164C23×C11—42no—
165C23×C11—44no—
166C23×C11—84no—
167C23×C11#12414yes—
168C23×C11C22×D411yescharacteristic
169C23×C11C22×D412yes—
170Q8×C11—24no—
171Q8×C11—24no—
172Q8×C11—44no—
173Q8×C11—88no—
174D4×C11—24no—
175D4×C11—24no—
176D4×C11—48no—
177D4×C11—48no—
178D4×C11—44no—
179D4×C11—88no—
180C2×C4×C11—28no—
181C2×C4×C11—24no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—48no—
185C2×C4×C11—48no—
186C2×C4×C11—84no—
187C2×C4×C11#12418yes—
188C2×C4×C11#12414yes—
189C2×C4×C11C22×D418yes—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4114yes—
193C2×C4×C11C2×#4112yes—
194C2×C4×C11C2×#4112yes—
195C2×C4×C11C2×#4114yes—
196C2×C4×C11C2511yescharacteristic
197C8×C11—22no—
198C8×C11—22no—
199C8×C11—24no—
200C22×#41C22×C1112yes—
201C22×M16C22×C1111yescharacteristic
202C23×C8C22×C1111yescharacteristic
203#544—22no—
204#544C22×C1118yescomplemented
205#543—22no—
206#537—22no—
207#536C22×C1114yes—
208#535C22×C1114yes—
209#534—22no—
210#533—24no—
211#533C22×C1114yescomplemented
212#532C22×C1114yes—
213#525—24no—
214C2×#117C22×C1112yes—
215C2×#117C22×C1111yescharacteristic
216#491C22×C1118yescomplemented
217#490C22×C1118yescomplemented
218#489C22×C11116yescomplemented
219#488C22×C11116yescomplemented
220#487C22×C1118yescomplemented
221#486C22×C1118yescomplemented
222#419C22×C1114yescomplemented
223#418C22×C1114yescomplemented
224#417C22×C1118yes—
225#416C22×C1118yes—
226#416C22×C1114yescomplemented
227#416C22×C1118yescomplemented
228#416C22×C1114yescomplemented
229C2×#103C22×C1114yescomplemented
230C2×#102C22×C1114yescomplemented
231#405C22×C1118yescomplemented
232C2×#97C22×C1112yescomplemented
233C2×C4×C8C22×C1112yescomplemented
234C22×C11—22no—
235C22×C11—24no—
236C22×C11—44no—
237C22×C11—48no—
238C22×C11—44no—
239C22×C11—88no—
240C22×C11C2×#12414yes—
241C22×C11C2×#12412yes—
242C22×C11C23×D411yescharacteristic
243C4×C11—28no—
244C4×C11—48no—
245C4×C11—44no—
246C4×C11C2×#12412yes—
247C4×C11C2×#12414yes—
248C4×C11C22×#4111yescharacteristic
249C4×C11C22×#4111yescharacteristic
250C2×#41—22no—
251C2×#41—22no—
252C2×#41—28no—
253C2×#41—28no—
254C2×#41C23×C1114yes—
255C2×#41C23×C1114yes—
256C22×Q8C23×C1112yes—
257C22×D4—22no—
258C22×D4C23×C1112yes—
259C23×C4—22no—
260C23×C4C23×C1111yescharacteristic
261C2×M16—24no—
262C2×M16C23×C1114yes—
263C22×C8—24no—
264C22×C8C23×C1111yescharacteristic
265C22×C8C23×C1111yescharacteristic
266C22×C8C23×C1114yes—
267C22×C8C23×C1112yes—
268C4⋊Q8—28no—
269C4⋊Q8C23×C1114yes—
270C4⋊Q8C23×C1118yes—
271#127C23×C1114yes—
272#125—28no—
273#125C23×C1118yes—
274#124C23×C1118yes—
275#123—28no—
276C22⋊Q8—28no—
277C22⋊Q8—28no—
278C22⋊Q8—216no—
279#121—28no—
280#121—28no—
281#120—28no—
282C4×Q8—28no—
283C4×D4—28no—
284#117—22no—
285#117—22no—
286#117D4×C1114yes—
287#117C23×C1114yes—
288#117C23×C1114yes—
289#117C23×C1114yes—
290C2×C4⋊C4D4×C1112yes—
291C2×C4⋊C4C23×C1114yes—
292C2×C22⋊C4—22no—
293C2×C22⋊C4D4×C1112yes—
294C2×C42—22no—
295C2×C42C23×C1112yes—
296#103C23×C1118yes—
297#103C23×C1118yes—
298#103C23×C11116yes—
299#102C23×C1118yes—
300#102C23×C1118yes—
301#102C23×C11116yes—
302#97C23×C1118yes—
303C4×C8C23×C1118yes—
304C2×C11—24no—
305C2×C11—22no—
306C2×C11—84no—
307C2×C11C22×#12411yescharacteristic
308C2×C11#358412yes—
309C24—22no—
310C24C2×D4×C1111yescharacteristic
311#41—28no—
312#41—28no—
313#41—28no—
314#41—28no—
315#41—48no—
316#41—48no—
317C2×Q8—22no—
318C2×Q8—28no—
319C2×Q8—24no—
320C2×Q8—24no—
321C2×Q8C24×C1114yes—
322C2×D4—24no—
323C2×D4—24no—
324C2×D4—22no—
325C2×D4—28no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—48no—
329C2×D4C24×C1114yes—
330C22×C4—22no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—48no—
335C22×C4C2×D4×C1114yes—
336C22×C4C2×D4×C1112yes—
337C22×C4C2×D4×C1111yescharacteristic
338C22×C4C11×#4114yes—
339C22×C4C11×#4114yes—
340C22×C4C24×C1111yescharacteristic
341C22×C4C24×C1112yes—
342M16—28no—
343C2×C8—28no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—24no—
347C2×C8C24×C1112yes—
348C2×C8C24×C1114yes—
349C2×C8C24×C1112yes—
350C4⋊C4—24no—
351C4⋊C4—28no—
352C4⋊C4—28no—
353C4⋊C4—216no—
354C4⋊C4C2×D4×C1118yes—
355C4⋊C4C24×C1118yes—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—216no—
359C22⋊C4C2×D4×C1118yes—
360C42—24no—
361C42—24no—
362C42C2×D4×C1114yes—
363C42C24×C1114yes—
364C11#6061211yescharacteristic, direct product factor, Sylow
365C23—24no—
366C23—42no—
367C23—44no—
368C23—84no—
369C23C11×#12414yes—
370C23C22×D4×C1111yescharacteristic
371C23C22×D4×C1112yes—
372Q8—24no—
373Q8—24no—
374Q8—44no—
375Q8—88no—
376D4—24no—
377D4—24no—
378D4—48no—
379D4—48no—
380D4—44no—
381D4—88no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—48no—
387C2×C4—48no—
388C2×C4—84no—
389C2×C4C11×#12418yes—
390C2×C4C11×#12414yes—
391C2×C4C22×D4×C1118yes—
392C2×C4C22×D4×C1112yes—
393C2×C4C22×D4×C1111yescharacteristic
394C2×C4C2×C11×#4114yes—
395C2×C4C2×C11×#4112yes—
396C2×C4C2×C11×#4112yes—
397C2×C4C2×C11×#4114yes—
398C2×C4C25×C1111yescharacteristic
399C8—22no—
400C8—22no—
401C8—24no—
402C22—22no—
403C22—24no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—88no—
408C22C2×C11×#12414yes—
409C22C2×C11×#12412yes—
410C22C23×D4×C1111yescharacteristic
411C4—28no—
412C4—44no—
413C4—48no—
414C4C2×C11×#12412yes—
415C4C2×C11×#12414yes—
416C4C22×C11×#4111yescharacteristic
417C4C22×C11×#4111yescharacteristic
418C2—24no—
419C2—22no—
420C2—84no—
421C2C22×C11×#12411yescharacteristic
422C2C11×#358412yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
prime radicalC11×#3449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3458C2semidirect
3. C11×#3137C2semidirect
4. C11×#3136C2semidirect
5. C11×#3135C2semidirect
6. C11×#3131C2semidirect
7. C11×#2896C2semidirect
8. C2×C11×#416C2semidirect
9. C2×C11×#405C2semidirect
14. C11×#544C22semidirect
21. C11×#533C22semidirect
26. C11×#491C22semidirect
27. C11×#490C22semidirect
28. C11×#489C22semidirect
29. C11×#488C22semidirect
30. C11×#487C22semidirect
31. C11×#486C22semidirect
32. C11×#419C22semidirect
33. C11×#418C22semidirect
36. C11×#416C22semidirect
37. C11×#416C22semidirect
38. C11×#416C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#102C22semidirect
41. C11×#405C22semidirect
42. C2×C11×#97C22semidirect
43. C2×C4×C8×C11C22semidirect
98. #60612C11direct (N × H)
154. #3458C2×C11semidirect
156. #3137C2×C11semidirect
157. #3136C2×C11semidirect
158. #3135C2×C11semidirect
159. #3131C2×C11semidirect
160. #2896C2×C11semidirect
161. C2×#416C2×C11semidirect
162. C2×#405C2×C11semidirect
204. #544C22×C11semidirect
211. #533C22×C11semidirect
216. #491C22×C11semidirect
217. #490C22×C11semidirect
218. #489C22×C11semidirect
219. #488C22×C11semidirect
220. #487C22×C11semidirect
221. #486C22×C11semidirect
222. #419C22×C11semidirect
223. #418C22×C11semidirect
226. #416C22×C11semidirect
227. #416C22×C11semidirect
228. #416C22×C11semidirect
229. C2×#103C22×C11semidirect
230. C2×#102C22×C11semidirect
231. #405C22×C11semidirect
232. C2×#97C22×C11semidirect
233. C2×C4×C8C22×C11semidirect
364. C11#60612direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#34582
C11×#34492
C11×#31372
C11×#31362
C11×#31352
C11×#31312
C11×#28962
C2×C11×#4162
C2×C11×#4052
#6061211